An Introduction to Functional Programming using Haskell

An Introduction to Functional Programming using Haskell Michel Rijnders <mies@tty.nl>

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Main Features purely functional lazy higher order strongly typed general purpose

History September 1987 FPCA “design by committee” P. Hudak, J. Hughes, S. Peyton Jones, and P. Wadler: “A History of Haskell: Being Lazy With Class” (2007)

Main Difference mainstream languages are all about state functional programming is all about values

Computation all computation is done via the evaluation of EXPRESSIONS to yield VALUES every value has an associated TYPE

Types basic types: Char, Bool, Int, Integer, Double composite types lists: [Char], [Int], [[Char]] tuples: (String,Int)

Function Types square :: Integer -> Integer (&&) :: Bool -> Bool -> Bool length :: [a] -> Int (:) :: a -> [a] -> [a]

Function Deﬁnitions fac :: Int -> Int fac n = if n == 0 then 1 else n * fac (n - 1)

Guards -- guards fac’ :: Int -> Int fac’ n | n == 0 = 1 | otherwise = n * fac’ (n - 1)

Pattern Matching -- pattern matching fac’’ :: Int -> Int fac’’ 0 = 1 fac’’ n = n * fac’’ (n - 1)

Exercises Template -- file: Main.hs module Main where import Prelude hiding (sum,length) sum :: [Int] -> Int ... length :: [a] -> Int ...

List Patterns [] xs (x:xs) (x:_) (_:xs) (_:_)

Summary computation types functions guards pattern matching list comprehensions

Coming Up programming with lists higher-order functions type classes algebraic types

List Functions (:) :: a -> [a] -> [a] tail, init :: [a] -> [a] (++) :: [a] -> [a] -> [a] replicate :: Int -> a -> [a] (!!) :: [a] -> Int -> [a] take, drop :: concat :: [[a]] -> [a] Int -> [a] -> [a] length :: [a] -> Int splitAt :: Int -> [a] -> ([a],[a]) head, last :: [a] -> a

More List Functions repeat :: a -> [a] and, or :: [Bool] -> Bool reverse :: [a] -> [a] sum, product :: zip :: [Int] -> Int [a] -> [b] -> [(a,b)] [Float] -> Float unzip :: [(a,b)] -> ([a],[b])

Programming with Lists Prelude> :load Sprite *Sprite> print glider .#. ..# ### [(),(),()] *Sprite> print (flipH glider) ### ..# .#. [(),(),()]

Sprite.hs flipH :: Picture -> Picture flipH pic = reverse pic flipV :: Picture -> Picture flipV pic = [ reverse line | line <- pic ]

Higher Order Functions functions as arguments functions as results or both

Higher Order Functions patterns of computation mapping: transforming elements ﬁltering: selecting elements folding: combining elements

Mapping and Filtering map :: (a -> b) -> [a] -> [b] ﬁlter :: (a -> Bool) -> [a] -> [a] zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]

Folding foldl :: (a -> b -> a) -> a -> [b] -> a foldl1 :: (a -> b -> a) -> [b] -> a foldr :: (a -> b -> b) -> b -> [a] -> b foldr1 :: (a -> a -> a) -> [a] -> a

Type Classes type class: a collection of of types over which certain functions are deﬁned equality class Eq (==) :: (Eq a) => a -> a -> Bool (/=) :: (Eq a) => a -> a -> Bool

Declaring a Class class Visible a where toString :: a -> String size :: a -> Int class Eq a where (==), (/=) :: a -> a -> Bool x /= y = not (x == y) x == y = not (x /= y)

Deﬁning an Instance instance Visible Char where toString ch = [ch] size _ = 1 instance Eq Bool where True == True = True False == False = True _ == _ = False

Derived Classes class Eq a => Ord a where (<), (<=), (>), (>=) :: a -> Bool max, min :: a -> a -> a compare :: a -> a -> Ordering

Built-In Classes Eq Ord Enum Show Read

Product Types data People = Person Name Age type Name = String type Age = Int data Shape = Circle Double | Rectangle Float Float

Recursive Algebraic Types data Expr = Lit Int | Add Expr Expr | Sub Expr Expr data Tree a = Node (Tree a) (Tree a) | Leaf a

More? http://haskell.org/ G. Hutton: Programming in Haskell (Cambridge University Press) B. O’Sullivan, J. Goerzen, D. Stewart: Real World Haskell (O’Reilly)

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An Introduction to Functional Programming using Haskell

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